An application of Berman's work on pool-model invariants in analyzing indistinguishable models for whole-body cholesterol metabolism

Berman and Schoenfeld used matrix transformations to study unidentifiable pool models. It is possible to use the method to examine if two models are output-indistinguishable, that is, if given the nature of tracer injections and observations, the two models have the same responses. The method is applied to two three-pool models for whole-body cholesterol metabolism. The indistinguishability of a mammillary model from a catenary model is proved using matrix transformations. The method is used in two ways, directly as well as after simplifying the problem. The two ways, as well as an analysis of the converse, help to show how the method is to be applied as well as the strengths and weaknesses of the method.